Near Maximum-Likelihood Performance of Some New Cyclic Codes Constructed in the Finite-Field Transform Domain

TL;DR

This paper demonstrates that certain cyclic codes constructed in the finite-field transform domain can achieve near maximum-likelihood decoding performance by optimizing their parity-check matrices, improving decoding accuracy.

Contribution

It introduces a novel technique of replacing dual codewords in parity-check matrices to enhance iterative decoding performance of cyclic codes.

Findings

Maximum-likelihood performance achieved for specific cyclic codes

Performance improvement through dual codeword substitution

Technique applicable to various cyclic code parameters

Abstract

It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the iterative decoder can be improved by substituting some of the dual code codewords in the parity-check matrix with other dual code codewords formed from linear combinations. This technique can bring the performance of a code closer to its maximum-likelihood performance, which can be derived from the erroneous decoded codeword whose euclidean distance with the respect to the received block is smaller than that of the correct codeword. For (63,37), (93,47) and (105,53) cyclic codes, the maximum-likelihood performance is realised with this technique.